In an acute-angled triangle ABC (AC = CB), the segment AF is the height.

In an acute-angled triangle ABC (AC = CB), the segment AF is the height. It is known that AC = 5cm, BF = 2cm. Calculate the cosine of the angle ACF.

1. The AC side of the ABC triangle is equal to the BC side according to the problem statement:

AC = BC = 5 cm.

2. We calculate the length of the segment CF:

СF = ВС- ВF = 5 – 2 = 3 cm.

3. In a right-angled triangle ACF, the leg CF is adjacent to the angle ACF, the AC side of this triangle is the hypotenuse. Their ratio is the cosine of the ACF angle.

4. Calculate the cosine of the angle ACF:

CF / AC = 3/5 = 0.6.

Answer: The cosine of the angle ACF is 0.6.